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基于非饱和多孔介质动力方程,研究了充满2种流体的非饱和多孔介质动力响应问题,并分别给出了2种边界条件作用下非饱和半无限多孔介质一维瞬态响应积分形式解。首先,运用正弦与余弦变换法将偏微分方程组变换为常微分方程组。然后,运用状态空间法求解此常微分方程组,得到变换域内解析解。最后,通过正弦与余弦反变换,给出非饱和半无限多孔介质一维瞬态响应积分形式解。该方法的优点是积分解中被积函数为实函数,给数值计算带来极大的方便。通过算例分析,验证了本文结果的正确性,证实了非饱和多孔介质内存在3种类型压缩波,分析了3类压缩波作用下多孔介质内固体和2种流体间的相位关系。
Based on the dynamic equation of unsaturated porous media, the dynamic response of unsaturated porous media saturated with two fluids is studied. The two-dimensional transient response integral solutions of unsaturated semi-infinite porous media under two kinds of boundary conditions are given respectively. First, transform the system of partial differential equations into the system of ordinary differential equations by using sine and cosine transform. Then, the state space method is used to solve the ordinary differential equations, and the analytical solution in the transformation domain is obtained. Finally, by means of the inverse sine and cosine transform, the one-dimensional transient response integral form solution for unsaturated semi-infinite porous media is given. The advantage of this method is that the integral function in the integral solution is a real function, which brings great convenience to numerical calculation. Through the example analysis, the correctness of the results in this paper is verified. It is confirmed that there are three types of compressional waves in the unsaturated porous media. The phase relationship between the solids and two fluids in the porous media under three kinds of compressional waves is analyzed.